Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant

In this paper, we consider the so-called p-system with linear damping on quadrant. We show that for a certain class of given large initial data (v0(x),u0(x)), the corresponding initial–boundary value problem admits a unique global smooth solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically, at the Lp (2⩽p⩽∞) optimal decay rates, to the corresponding nonlinear diffusion wave (v¯(x,t),u¯(x,t)) which satisfies (1.9) provided the corresponding prescribed initial error function (V0(x),U0(x)) lies in (H3(R+)∩L1(R+))×(H2(R+)∩L1(R+)).

[1]  Kenji Nishihara,et al.  Boundary Effect on Asymptotic Behaviour of Solutions to the p-System with Linear Damping , 1999 .

[2]  S. Yu,et al.  Zero-Dissipation Limit of Solutions with Shocks for Systems of Hyperbolic Conservation Laws , 1999 .

[3]  Lizhi Ruan,et al.  Existence of global smooth solution to the initial boundary value problem for p-system with damping , 2009 .

[4]  Hailiang Li,et al.  Asymptotic behavior of solutions to quasilinear hyperbolic equations with nonlinear damping , 2003 .

[5]  Tai-Ping Liu,et al.  Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping , 1992 .

[6]  Kenji Nishihara,et al.  Convergence Rates to Nonlinear Diffusion Waves for Solutions of System of Hyperbolic Conservation Laws with Damping , 1996 .

[7]  Ronghua Pan,et al.  Darcy's law as long-time limit of adiabatic porous media flow , 2006 .

[8]  Kenji Nishihara,et al.  Asymptotic Behavior of Solutions of Quasilinear Hyperbolic Equations with Linear Damping , 1997 .

[9]  ASYMPTOTIC BEHAVIOR FOR SCALAR VISCOUS CONSERVATION LAWS WITH BOUNDARY EFFECT , 1997 .

[10]  Kenji Nishihara,et al.  Lp-Convergence Rate to Nonlinear Diffusion Waves for p-System with Damping , 2000 .

[11]  Hongxia Liu,et al.  Asymptotic stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas with boundary , 1999 .

[12]  Feimin Huang,et al.  Digital Object Identifier (DOI) 10.1007/s00205-002-0234-5 Convergence Rate for Compressible Euler Equations with Damping and Vacuum , 2022 .

[13]  Huijiang Zhao.  Asymptotic Behaviors of Solutions of Quasilinear Hyperbolic Equations with Linear Damping II , 2000 .

[14]  Changjiang Zhu.  Convergence rates to nonlinear diffusion waves for weak entropy solutions to p -system with damping , 2003 .

[15]  Changjiang Zhu,et al.  Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms , 1997, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[16]  Huijiang Zhao,et al.  Convergence to Strong Nonlinear Diffusion Waves for Solutions of p-System with Damping , 2001 .

[17]  Propagation of a Stationary Shock Layer in the Presence of a Boundary , 1997 .

[18]  Constantine M. Dafermos,et al.  A system of hyperbolic conservation laws with frictional damping , 1995 .

[19]  Changjiang Zhu,et al.  Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping , 2006 .

[20]  西田 孝明,et al.  Nonlinear hyperbolic equations and related topics in fluid dynamics , 1978 .

[21]  Ming Mei,et al.  Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation laws with damping , 2000 .

[22]  L. Hsiao,et al.  Construction and Qualitative Behavior of the Solution of the Perturbated Riemann Problem for the System of One-Dimensional Isentropic Flow with Damping , 1995 .

[23]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[24]  Ming Mei,et al.  Convergence to Travelling Fronts of Solutions of the p‐System with Viscosity in the Presence of a Boundary , 1999 .

[25]  Tai-Ping Liu,et al.  Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves , 1998 .

[26]  Ming Mei,et al.  Optimal Convergence Rates to Diffusion Waves for Solutions of the Hyperbolic Conservation Laws with Damping , 2005 .

[27]  Changjiang Zhu.  Asymptotic Behavior of Solutions for p-System with Relaxation , 2002 .